2,068 research outputs found
Commutative Energetic Subsets of BCK-Algebras
The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal
The Octonions
The octonions are the largest of the four normed division algebras. While
somewhat neglected due to their nonassociativity, they stand at the crossroads
of many interesting fields of mathematics. Here we describe them and their
relation to Clifford algebras and spinors, Bott periodicity, projective and
Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also
touch upon their applications in quantum logic, special relativity and
supersymmetry.Comment: 56 pages LaTeX, 11 Postscript Figures, some small correction
Ordered homomorphisms and kernels of ordered BCI-algebras
Recently Yang-Roh-Jun introduced the notion of ordered BCI-algebras as a
generalization of BCI-algebras. They also introduced the notions of
homomorphisms and kernels of ordered BCI-algebras and investigated related
properties. Here we extend their investigation to ordered homomorphisms, i.e.,
order-preserving homomorphisms. To this end, the notions of ordered
homomorphism and kernel of ordered BCI-algebras are first defined. Next,
properties associated with (ordered) subalgebras, (ordered) filters and direct
products of ordered BCI-algebras are addressed
Coderivations of Ranked Bigroupoids
The notion of (co)derivations of ranked bigroupoids is discussed by Alshehri et al. (in press), and their generalized version is studied by Jun et al. (under review press). In particular, Jun et al. (under review press) studied coderivations of ranked bigroupoids. In this paper, the generalization of coderivations of ranked bigroupoids is discussed. The notion of generalized coderivations in ranked bigroupoids is introduced, and new generalized coderivations of ranked bigroupoids are obtained by combining a generalized self-coderivation with a rankomorphism. From the notion of (X,∗,&)-derivation, the existence of a rankomorphism of ranked bigroupoids is established
Hypervector Spaces Based on Intersectional Soft Sets
The notion of int-soft subfields, int-soft algebras over int-soft subfields, and int-soft hypervector spaces are introduced, and their properties and characterizations are considered. In connection with linear transformations, int-soft hypervector spaces are discussed
Fuzzy implicative hyper BCK-ideals of hyper BCK-algebras
We consider the fuzzification of the notion of implicative hyper
BCK-ideals, and then investigate several properties.
Using the concept of level subsets, we give a
characterization of a fuzzy implicative hyper BCK-ideal. We state
a relation between a fuzzy hyper BCK-ideal and a fuzzy implicative
hyper BCK-ideal. We establish a condition for a fuzzy hyper
BCK-ideal to be a fuzzy implicative hyper BCK-ideal. Finally, we
introduce the notion of hyper homomorphisms of hyper
BCK-algebras, and discuss related properties
Zero-frequency Bragg gap by spin-harnessed metamaterial
The Bragg gap that stops wave propagation may not be formed from zero or a very low frequency unless the periodicity of a periodic system is unrealistically large. Accordingly, the Bragg gap has been considered to be inappropriate for low frequency applications despite its broad bandwidth. Here, we report a new mechanism that allows formation of the Bragg gap starting from a nearly zero frequency. The mechanism is based on the finding that if additional spin motion is coupled with the longitudinal motion of a mass of a diatomic mechanical periodic system, the Bragg gap starting from a nearly zero frequency can be formed. The theoretical analysis shows that the effective mass and stiffness at the band gap frequencies are all positive, confirming that the formed stop band is a Bragg gap. The periodic system is realized by a spin-harnessed metamaterial which incorporates unique linkage mechanisms. The numerical and experimental validation confirmed the formation of the low-frequency Bragg gap. The zero-frequency Bragg gap is expected to open a new way to control hard-to-shield low-frequency vibration and noise
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